Wave filter



April 1935. s. DARLINGTON l,996,504

WAVE FILTER Filed April 12, 1933 AAAAAAAAAA 2 vvvvvv'vv' 4 INVEN TOP 5.DARL ING TON A TTC/?NEY Patented Apr. 2, 1935 UNITED STATES PATENTOFFICE WAVE FILTER Application April 12, 1933, Serial No. 665,685

4 Claims.

This invention relates to wave filters, particularly of the type usingpiezoelectric crystals as impedance elements, and has for its principalobject reduction of the number of crystals required for the provision ofa desired transmission characteristic.

A type of piezoelectric crystal wave filter which has proven to behighly practical where relatively wide transmission bands are required,consists of a=symmetrical lattice network the branches of which areequal in pairs and comprise only combinations of piezoelectric crystalsand capacities, in combination with external inductances connectedeither in series or in shunt at each end of the lattice. The lattices insuch filters may include crystals in all four branches or, in. simplercases, one pair of branches may comprise only capacities and the otherpair a single crystal. In any case at least two crystals are required.

In accordance with this invention the practical construction of filtersof this type is Simplified by substituting a simple condenser for one ofthe lattice branches which includes a crystal and modifying the crystalof the other corresponding branch to compensate for the substitution.This results in an unsymmetrical lattice having one pair of equalbranches which may or may not include piezoelectric crystals and a pairof unequal branches one of which consists of a simple capacity and theother of which includes a piezoelectric crystal. The filters of theinvention include unsymmetrical lattice networks of this type incombination with external inductances connected either in series or inshunt at each end of the lattice.

The invention will be more fully understood from the following detaileddescription and by reference to the appended drawing of which:

Figs.1 and 2 are schematic diagrams illustrating a principle involved inthe invention;

Figs. 3 and 4 show respectively a filter in acooi-dance With theinvention and its symmetrical prototype;

Fig. 5 is a diagram representing the electrical properties of a crystal;and

Figs. 6 and 7 show respectively a modified network of the invention andits symmetrical prototype. t

Referring to the drawing, Figures 1 and 2 show respectively generalschematics of a symmetrical lattice and an unsymmetrical lattice of'thetype corresponding to the filters of the invention. In the former theline branch impedances are designated Z and the lattice branchimpedances Zz. In the latter the line branches also have the impedance Zbut the lattice branches have unequal impedances ZB and Zc respectively.In both figures the input terminals are marked l, 2, and theOutputterminals 3, 4.

The two networks may be made equivalent in respect of their imageimpedances and transfer constants provided the impedances ZB and Zc ofFig. 2 bear a certain required relationship to each other and to theimpedances Z and Z2. The required relationship may be determined from anexamination of the expressions for the transmission parameters of thetwo networks in terms of the branch impedances. The products of the opencircuit and short circuit impedances define the values of the imageimpedances and their ratios define the transfer constants. For thenetworks of Figs. 1 and 2 'the respective image impedances K and K2 havethe values The transfer constants 91 and 62 have the values and Therequirement that the two networks have the same image impedance givestanh 0 that for tanh 02. The relationship set forth in Equation (4) istherefore sufficient for the complete equivalence of the networks.

The network shown schematically in Fig. 3 represents a piezoelectriccrystal band pass filter in accordance with the invention which may bederived in the manner outlined above from the symgnetrical prototypenetwork shown in Fig. 4. In Fig. 3 the line branches of the lattice,corresponding to impedances Z, comprise piezoelectric crystals X shuntedby capacities G; The lattice branch corresponding to the imped; ance Zcof Fig. 2 consists of a simple capacity 'C and the branch correspond'ngto impedance ZB comprises a piezoelectric crystal Xe shunte'd by acapacity CB. External inductances of value d'esignated by L/2 are addedin series in each line at both ends of the lattice. These cooperate withthe crystals in determining the width of the band in the mannerdescribed in the copending application of W; P; Mason, Serial No. 653622, filed January 26, 1933.

The sym'metrical prototype network of Fig. 4 is similar in its structureexcept that the two lattice arms comprise similar crystals Xz shunted by'capacities Cz.

The crystal branches in each case comprise crystals shunted bycapacities. The crystals are preferably of quartz, cut and mounted inthe manner described in the above identified application and theshunting condensers are preferably small well insulated Variable aircondensers. The combination of the crystal and the shunt capacitycorresponds very accurately in its impedance characteristics to anelectrical impedance of the type illustrated schematically in Fig. 5,comprising the combination of an inductance L and capacity C connectedin series with a shunt capacity Co. The inductance L and the capacity Crepresent the piezoelectric properties of the crystal and the capacityCo represents the electrostatic capacity of the crystal electrodes plusthe external shunting capacity. A characteristic property of thecombination is that the effective shunting capacity Co is very large incomparison with the piezoelectric capacity C, its minimum value being atleast as great as 125 C.

On account of this large value of the capacity ratio the impedance ofthe crystal is characterized by a very sharp transition from a resonancecondition to an anti-resonance condition as the frequency is varied. Theresonance and the anti-resonance frequencies differ by a maximum of 0.4per cent, the resonance frequency being the lower. p n

Mathematically the impedance may be expressed by the formula resonancerespectively.

The design of a filter of the type shown in Fig. 3 is most readilyaccomplished by derivation from its sy'nmetrical prototype shown in Fig.4 by the general procedure 'outlined above. The

transmission characteristics and the design computation of the prototypenetwork are fully explained in the above mentioned copending applicationof W. P. Mason. Briefly the design procedure is as follows: Theinductances added external to the lattice are equivalent to inductancesof value L added in series with each branch. The combination of aninductance in series with a capacity shunted crystal gives a reactancecharacterized by resonances at two frequencies and an intermediateanti-resonance. The separation of these critical frequencies may be madesubstantially uniform by proportioning the inductance to resonate withthe total shunt capacity of the crystal at the crystal resonancefrequency and the amount of the separation may be controlled by varyingthe value of the shunt capacity. By giving the crystals appropriatenatural frequencies the location of the critical frequencies of thebranches may be controlled and by so allocating these frequencies thatthe lower resonance and the anti-resonance frequencies of one pair ofbranches coincide respectively with the anti-resonance and 'upper onancefrequencies of the 'other pair a 'single transmission band is obtained.

The derivation of the network of Fig. 3 from its prototype 'proceeds asfollows: The line branch impedances, Z, of the lattice and of it'sproto'- type can be 'expressed in terms of the critical frequencies bythe formula 1 .la jw o b (6) Where Col is the total shunt capacity "ofthe impedance and wie. and zou, 'correspond to-the resonance andanti-resonance frequencies' re'- spectively. The lattice branchimpedance Z'z of the prototype may be expressed by the similar formula vin which the quanttes C2o, wza, and wb correspond to the like'quan'titi'es in Equation '(7). The value of Zc which in Fig. 3 is asimple capacity is given by Substituting the values given above inEquation '(4) an expression is obtained for the value of the impedanceZb necessary to make the network -of Fig. 3 equivalent to its prototype.This expression is as follows:

The numerator and the denominator 'of this expression are of the 'fourthdegree -i'n w, but involveno odd degree terms. The expression 'therefore represents in general an impedance having two resonance and twoanti-reso`nance 'frequencies such as might be obtained by connecting twocrystals in series. I have found, however, that, by giving the capacity'C a particular value, a common factor can be removed from'the numeratorand the denominator leaving a 'simplified expression of the seconddegree in w 'which represents an impedance that can `be realized by acapacity shunted crystal.

If the numerator and the denominator of Equatien (9) be expanded 'andthe terms collected t will be found that the terms of zero degree arerespectively Expressions 10 and 11 may be transformed respectively to Asimple trial shows that the factor coz-(Cook 2o 2b is common to bothnumerator and denominator and its removal therefrom leaves theexpression The expression in Equation will correspond to an impedancethat can be realized by a capacity shunted crystal only if thefrequencies wa. and wb are separated by an amount less than 0.4 percent. I have found, however, from the computation of a sufficient numberof designs that the frequency separaton is within the required range solong as the prototype filter branches include only crystals asillustrated by Fig 3. The value of the capacity C in the capacity arm ofthe filter is obtainable from Equation 12. This, upon simplification, isa quadratic equation, which gives two values of C one of which is alwayspositive and the other always negative. The positive value must ofcourse be chosen.

A Simpler form of the invention is illustrated schematically in Fig. 6,the symmetrical prototype being shown in Fig. 7. In these networks theline branches of the lattices, i. e. the Z impedances, consist of simplecapacities Ci instead of capacity shunted crystals. The impedances ofthe other branches of Fig. 6 correspond to the respective branches ofFig. 3 and those of Fig. 7 to the respective branches of Fig. 4.

The prototype network is a'. band pass filter which will pass a singleband of frequencies provided the inductance L resonates with the linebranch capacity C at the anti-resonance of crystal capacity combinationX2C2 of the lattice branches. Preferably also the inductance L should besuch as to resonate with the total capacity of the shunted crystals atsome frequency close to the crystal resonance. This assures a highattenuation level both above and below the band. The design of theunsyrmetrcal filter of the invention from the constants of the prototypenetwork follows a similar procedure to that discussed in connection withFig. 3. The impedance Z of the line branches of the prototype lattice,and also of the lattice of Fig. 6, has the value 1 z-jzrc-" and thelattice branch impedance Zz of the prototype has the value given byEquation (7). The substitution of these values in Equation (4) givesdirectly for the impedance Zb an expression of the same form as Equation(15) in which the effective capacity and the critical frequencies havethe values In this case the capacity C may have a range of valueslimited only by the requirement that the critical frequencies wa and wbmust be sufficiently close together to correspond to the frequencies ofa capacity shunted crystal.

What is claimed is:

1. A broad band wave filter comprising a lattice network having linebranches of equal impedance, a lattice branch consisting of a simplecapacity, a second lattice branch comprising a piezoelectric crystal,and an inductance connected at each end of the lattice external thereto,the reactance of said inductance and the impedances of the branches ofsaid lattice network being proportioned with respect to each other toprovide a single transmission band between two preassigned frequencies.

2. A broad band filter in accordance with claim 1 in which theimpedances of the equal line branches of the lattice are constituted bysimple capacities.

3. A broad band filter in accordance with claim 1 in which theimpedances of the equal line branches are constituted by piezoelectriccrystals and capacities in shunt thereto.

4. A wave filter comprising a lattice network interconnecting a pair ofinput terminals and a pair of Output termnals, similar piezoelectriccrystals included as impedance elements in the line branches of saidlattice, a lattice branch including only a simple capacity, and a secondlattice branch including a piezoelectric crystal, the impedances of saidbranches being proportioned with respect to each other to provide asingle pass band between preassigned frequencies.

SIDNEY DARLINGTON.

